Download Chapter 6 Review on sections 6.1-6.8

Advanced Geometry Chapter 6.1-6.8 Review Sheet
Name:________________
For questions 1-8, determine whether the statement is ALWAYS,
SOMETIMES, or NEVER true.
1.
2.
3.
4.
5.
6.
7.
8.
Diagonals of a trapezoid are perpendicular.
Adjacent sides of a rectangle are congruent.
Opposite angles of a trapezoid are congruent.
Adjacent angles of a rhombus are supplementary and congruent.
Diagonals of a square are perpendicular.
A trapezoid is a type of parallelogram.
Both pairs of opposite angles of a parallelogram are congruent.
The diagonals of a parallelogram are congruent.
1.___________________
2.___________________
3.___________________
4.___________________
5.___________________
6.___________________
7.___________________
8.___________________
9. Find the values of x and y that ensures the quadrilateral is a
parallelogram. Show work in the space below.
9.___________________
10. Find x given the figure is a rectangle.
10.__________________
11. If PQRS is a rhombus and m∠PQT = 34 ,
Find m∠PQR.
11.__________________
12.__________________
12. In the diagram, trapezoid ABCD has median XY drawn. If AB=2x-3,
CD=4x-1, and XY=2x+5, what is the value of x?
13. In a parallelogram WXYZ, determine which of the following pairs of
angles are supplementary.
I. ∠Y and ∠Z
A. I only
II. ∠Xand ∠Z
III. ∠W and ∠Y
B. III only
C. I and II only D. I and III only
13.__________________
E. I, II, and III
14. Wayne is building a table with diagonal supports as shown below.
14.
A. How can he use a ruler to determine whether the table top is parallel
to the floor?
B. Suppose he finds the table top is parallel to the floor and the legs are
parallel to each other. How can he then use a ruler to determine
whether the table top is perpendicular to the leg?
A.___________________
_____________________
15. What special type of quadrilateral has the vertices M(3,4),
N(1,-6), P(6,-7), and Q(8,3)?
15.__________________
16. If a diagonal of MNOP divides MNOP into two equilateral triangles,
what kind of figure must MNOP be? Draw your figure below.
16.__________________
17. Figure XYZW is an isosceles trapezoid. Find m∠YZW.
17.__________________
B.___________________
_____________________
18. Write a two-column proof.
Given: ∠3 ≅ ∠6 ; ∠3 ≅ ∠4
Prove: Quadrilateral ABCD is a parallelogram
Statements
1._________________________
2._________________________
3._________________________
4._________________________
5._________________________
Reasons
1._________________________
2._________________________
3._________________________
4._________________________
5._________________________
19. Write a two-column proof.
Given: !ABCD ; ∠1 ≅ ∠2
Prove: △DAC ≅ △BCA
Statements
1._________________________
2._________________________
3._________________________
4._________________________
Reasons
1._________________________
2._________________________
3._________________________
4._________________________
20. Write a two-column proof.
Given: !PQRS ; PT ≅ UR
Prove: QT ≅ SU
Statements
1._________________________
2._________________________
3._________________________
4._________________________
5._________________________
Reasons
1._________________________
2._________________________
3._________________________
4._________________________
5._________________________
21. Find the missing angle.
21.__________________
22. Find the measure of an exterior angle of a regular 24-gon.
22.__________________
23. The sum of the angle measures of a polygon is 900 with n sides.
Find the number of sides, n.
23.__________________
24. The measure of an interior angle of a regular polygon is four times
the measure of an exterior angle of the same polygon. What is the
name of the polygon?
24.__________________
25. What additional pieces of information could be supplied to make
ABCD a parallelogram?
25.__________________
26. Can you prove that the quadrilateral is a parallelogram based on the
given information? Explain.
26.__________________
27. Decide whether the parallelogram is a rhombus, a rectangle, or a
square. Explain.
27.__________________
28. Which statement would be sufficient to prove that a quadrilateral is
a rhombus?
A. The quadrilateral has four congruent angles.
B. The quadrilateral has two pairs of parallel sides.
C. The quadrilateral has four congruent sides.
D. The quadrilateral has two pairs of congruent angles.
28.__________________
29. Write All, Some, or No for the blank. _____ kites have two pairs of
congruent sides.
29.__________________
30. Write All, Some, or No for the blank. _____ kites have congruent
diagonals.
30.__________________
31. Find EF in the trapezoid.
31. EF = _____________
32. Graph the given points. Use slope to determine the most precise
name for quadrilateral ABCD.
32.__________________
33. Give the coordinates for points D and S without using any new
variables.
33.
D (________,________)
S (________,________)
34. Give coordinates for points D and S without using any new variables. 34.
D (________,________)
S (________,________)
35.
35.
m∠1 = ______________
m∠2 =______________
m∠2